Clebsch–Gordan and Racah–Wigner Coefficients for a Continuous Series of Representations of ?q (??(2, ℝ))

By B. Ponsot, Jörg Teschner. 2000

165 citations recorded by the source corpus.

Abstract: The decomposition of tensor products of representations into irreducibles is studied for a continuous family of integrable operator representations of Uq(sl(2,ℝ). It is described by an explicit integral transformation involving a distributional kernel that can be seen as an analogue of the Clebsch–Gordan coefficients. Moreover, we also study the relation between two canonical decompositions of triple tensor products into irreducibles. It can be represented by an integral transformation with a kernel that generalizes the Racah–Wigner coefficients. This kernel is explicitly calculated.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/73df34f9f0354c96c39a691b8ba52e21487f29a8

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In Algebra and Number Theory

1. J. Teschner
2. V. Spiridonov
3. A. Bytsko
4. E. Martinec
5. B. Ponsot
6. G. Vartanov
7. Eric M. Rains
8. S. Ole Warnaar

In Geometry and Topology

1. J. Teschner
2. V. Spiridonov
3. E. Martinec
4. A. Bytsko
5. B. Ponsot
6. A. Zamolodchikov
7. Y. Nakayama
8. H. Verlinde

In Mathematical Physics

1. J. Teschner
2. E. Martinec
3. V. Spiridonov
4. A. Bytsko
5. B. Ponsot
6. Y. Nakayama
7. Marika Taylor
8. H. Verlinde

Citations in the corpus

• Liouville field theory on a pseudosphere (2001, background): “For “ordinary” boundary conditions in boundary LFT this program has been started in [13] (see also [21, 22 , 20]).”
• Quantization of models with non-compact quantum group symmetry: Modular XXZ magnet and lattice sinh-Gordon model (2006, methodology): “αs αt + PT2 . (D.46)”
• Boundary Liouville field theory: boundary three-point function (2002, methodology): “where the b-Racah-Wigner coefficients that appear on the rig ht hand side have been modified w.r.t. to those considered in [ 12 ] according to”
• Essays on the theory of elliptic hypergeometric functions (2008, methodology): “These functions, related to the Barnes gamma function of the second order, are actively used in the modern mathematical physics in the description of quantum integrable models and representations of quantum algebras [19, 20, 21, 22 , 23, 24].”
• The Annular Report on Non-Critical String Theory (2003, background): “this becomes a hidden, internal quantum group symmetry Uq(sl(2, R)) [91, 92, 93, 94 ] (for reviews, see [95, 40, 96]).”